Erlang loss bounds for OT-ICU systems

N.M. van Dijk, N. Kortbeek*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

28 Citations (Scopus)
115 Downloads (Pure)


In hospitals, patients can be rejected at both the operating theater (OT) and the intensive care unit (ICU) due to limited ICU capacity. The corresponding ICU rejection probability is an important service factor for hospitals. Rejection of an ICU request may lead to health deterioration for patients, and for hospitals to costly actions and a loss of precious capacity when an operation is canceled. There is no simple expression available for this ICU rejection probability that takes the interaction with the OT into account. With c the ICU capacity (number of ICU beds), this paper proves and numerically illustrates a lower bound by an $M|G|c|c$ system and an upper bound by an $M|G|c-1|c-1$ system, hence by simple Erlang loss expressions. The result is based on a product form modification for a special OT–ICU tandem formulation and proved by a technically complicated Markov reward comparison approach. The upper bound result is of particular practical interest for dimensioning an ICU to secure a prespecified service quality. The numerical results include a case study.
Original languageEnglish
Pages (from-to)253-280
Number of pages28
JournalQueueing systems
Issue number1-4
Publication statusPublished - 26 Nov 2009


  • MSC-60J27
  • MSC-60K25
  • MSC-90B22
  • Tandem queues
  • Operating rooms
  • Capacity planning
  • Markov reward approach
  • Intensive care unites
  • Health services


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